How to mask a clip based on the key of another

I have two videos overlapped on one another. One is a white shadow of the object against a black background. The other is of the colour of the object.

I've masked the white shadow with a luma keyer so only the white parts are visible. I want to mask the colourised video using the white shadow as a mask, so that all semi transparent parts are recognised from the white shadow. So I can then place the colourised video against backgrounds successfully. How do I do this?